Question

A set of n values x₁, x₂, .......x_n has standard deviation σ. The standard deviation of n values ax₁, ax₂, ...., a_xn is ________________.

Answer 1

For x₁, x₂, ........x_n , Standard deviation is $\sigma$ (given)
Then variance of x₁, x₂, ..........x_n is ${\sigma }^2$
For ax₁, ax₂, ...........ax_n ,
Variance is given by a²Var(x₁, x₂, ........x_n)²
i.e a²${\sigma }^2$.
$\therefore$ Standard deviation of ax₁, ax₂, ...........ax_{n
$$\begin{gathered} =\sqrt{\mathrm{Variance}(a{x}_1,a{x}_2,......a{x}_n)} \\ =\sqrt{a^2{\sigma }^2} \end{gathered}$$}
Standard deviation of ax₁, ax₂, .......ax_n = |a|σ